Depinning of KPZ interfaces in fractional Brownian landscapes

We explore the critical dynamics of driven interfaces propagating through a two-dimensional disordered medium with long-range spatial correlations, modeled using fractional Brownian motion (FBM). Departing from conventional models with uncorrelated disorder, we introduce quenched noise fields characterized by a tunable Hurst exponent [Formula: see text], allowing systematic control over the spatial structure of the background medium. The interface evolution is governed by a quenched Kardar-Parisi-Zhang (QKPZ) equation modified to account for correlated disorder, namely QKPZ[Formula: see text]. Through analytical scaling analysis, we uncover how the presence of long-range correlations reshapes the depinning transition, alters the critical force [Formula: see text], and gives rise to a family of critical exponents that depend continuously on [Formula: see text]. Our findings reveal a rich interplay between disorder correlations and the non-linearity term in QKPZ[Formula: see text], leading to a breakdown of conventional universality and the emergence of nontrivial scaling behaviors. The exponents are found to change by H in the anticorrelation regime ([Formula: see text]), while they are nearly constant in the correlation regime ([Formula: see text]), suggesting a robust-universal behavior for the latter. By a comparison with the quenched Edwards-Wilkinson model, we study the effect of the non-linearity term in the QKPZ[Formula: see text] model.